Nonlinear interaction of longitudinal and transverse vibrations of a rod at an internal combinational resonance in view of opto-thermal excitation of N/MEMS

Abstract

In this paper, the character of coupled longitudinal-flexural vibrations of a rod is investigated in the case of an internal combinational resonance between two flexural and lower longitudinal vibration modes. An approximate analytical solution is obtained by a multiple time-scales method applied directly to a system of nonlinear partial differential equations. It is shown that the initial perturbation in the longitudinal direction can effectively excite bending vibration modes, which, on the whole, leads to a longitudinal-transverse beating regime with noticeable amplitudes. It is noted that the period and amplitude of these beats substantially depend on the frequency detuning parameter between the sum of the bending vibration frequencies and the longitudinal vibration frequency. This effect can be used as a new principle of operation of opto-thermally excited N/MEMS resonant sensors.